Rhythm of the Deep: Two-Tier Combinatorial Structure in Sperm Whale Codas Revealed by Acoustic Unit Induction

[Submitted on 15 Jun 2026 (v1), last revised 1 Aug 2026 (this version, v2)]

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Abstract:Sperm-whale codas are conventionally described as recurring click-count and timing patterns. We show instead that their waveforms contain a two-tier combinatorial acoustic organization. Recurring click units combine with inter-click rhythm to form coda units, and recurring coda units exhibit additional sequence-level dependence under a different acoustic carrier. Using 1,483 recordings, eight families of frozen audio encoders induce click and coda inventories. Held-out transfer, matched nulls, destructive waveform counterfactuals, expert timing baselines, and explicit abstention separate supported structure from shared encoder shortcuts. Click-token composition predicts induced coda identity with a median normalized mutual-information lift of 0.380, including when events are detected without published click times or counts. Stable click order is weak, whereas rhythm predicts coda-representation distance after the exact click-token multiset is fixed. At the second tier, coda tokens show 0.132 bits of incremental lag-2 dependence under the prespecified categorical estimator. Two expert-inspired rhythm representations do not recover the positive component. Coda identity is also more tempo-stable than click identity. These results change the acoustic description of codas from a single prescribed rhythm inventory to layered waveform organization. The controlled-induction framework provides a general method for discovering and falsifying combinatorial structure in under-annotated audio.

Submission history

From: Mudit Sinha [view email]
[v1] Mon, 15 Jun 2026 00:49:18 UTC (920 KB)
[v2] Sat, 1 Aug 2026 06:25:08 UTC (223 KB)